7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 4\",\"description\":\"One-variable data: distributions, mean, median, range, and variability.\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-one-variable-data-quiz-4\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Problem-Solving and Data Analysis: One-variable data-Distributions and measures of center and spread\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Quiz 4\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-one-variable-data-quiz-4\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","div",null,{"className":"container mx-auto px-4 py-8 md:py-12","children":[["$","div",null,{"className":"mb-12","children":["$undefined",["$","div",null,{"className":"mb-8","children":["$","h1",null,{"className":"text-4xl md:text-5xl lg:text-6xl font-bold text-gray-900 mb-4","children":"Quiz 4"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

One-variable data: distributions, mean, median, range, and variability.

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Practice quiz on distributions and measures of center and spread for PSAT 8-9.

"},"excerpt":{"rendered":"

One-variable data: distributions, mean, median, range, and variability.

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Advanced","categorie":"Problem-Solving and Data Analysis: One-variable data-Distributions and measures of center and spread","nombre_questions":10,"score_minimum":70,"ordre_questions":"Aleatoire","questions":[{"id":"cmrk8f0570y01jg8w9cg3852n","texte_question":"

For which of the following data sets is the mean greater than the median?

","type_question":"QCM","explication":"

Compare the mean and median of each data set.

For $$6,6,6,6,6,6,6$$, the mean and median are both $$6$$.

For $$2,4,6,8,10,12,14$$, the data set is evenly spaced, so the mean and median are both $$8$$.

For $$3,6,12,24,48,96,192$$, the median is the middle value.

The median is $$24$$.

Find the mean:

$$(3+6+12+24+48+96+192)\\div7=381\\div7$$

$$381\\div7\\approx54.43$$

Since $$54.43$$>$$24$$, the mean is greater than the median.

Final answer: $$3,6,12,24,48,96,192$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$6,6,6,6,6,6,6$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$2,4,6,8,10,12,14$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$3,6,12,24,48,96,192$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$5,50,50,50,50,50,50$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f05a0y07jg8w99io7a6e","texte_question":"

Data set A consists of 8 positive integers less than 80. The list below shows 7 of them:

$$41,42,39,38,40,43,41$$

The mean of these 7 integers is $$40$$. If the mean of all 8 integers is an integer greater than $$40$$, what is the value of the largest integer in data set A?

","type_question":"TexteLibre","explication":"

The mean of the first $$7$$ integers is $$40$$.

So, the sum of the first $$7$$ integers is:

$$7\\cdot40=280$$

Let the missing integer be $$x$$.

The sum of all $$8$$ integers is: $$280+x$$

The mean of all $$8$$ integers is: $$\\frac{280+x}{8}$$

This mean must be an integer greater than $$40$$.

Since $$280$$ is divisible by $$8$$, $$x$$ must also be divisible by $$8$$.

Also, the missing integer must be less than $$80$$ and greater than $$40$$.

The possible values are:

$$48,56,64,72$$

The largest possible missing value is $$72$$.

Since $$72$$ is greater than all the other listed values, the largest integer in the data set is $$72$$.

Final answer: $$72$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f05c0y0ajg8wcl62agjz","texte_question":"$18","type_question":"QCM","explication":"

Find the mean first. The total frequency is:

$$a+3a+5a+3a+a=13a$$

Find the weighted sum:

$$1(a)+2(3a)+3(5a)+4(3a)+5(a)$$

$$=a+6a+15a+12a+5a$$

$$=39a$$

The mean is:

$$\\frac{39a}{13a}=3$$

Now find the median.

The distribution is symmetric around $$3$$.

Also, the middle value of the data set is $$3$$.

So, the median is: $$3$$

The mean minus the median is:

$$3-3=0$$

Final answer: $$0$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$0$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$0.5$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$1$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f05f0y0gjg8wqr70cqxx","texte_question":"

If $$a$$ is the mean and $$b$$ is the median of eleven consecutive integers, what is the value of $$|a-b|$$?

","type_question":"TexteLibre","explication":"

For any odd number of consecutive integers, the median is the middle value.

There are $$11$$ consecutive integers, so the median is the $$6$$th value.

The mean of consecutive integers is also the middle value.

So:

$$a=b$$

Therefore:

$$|a-b|=0$$

Final answer: $$0$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f05h0y0jjg8wskptft8l","texte_question":"$19","type_question":"TexteLibre","explication":"

Group A has $$10$$ players, so the median is the average of the $$5$$th and $$6$$th scores. List group A in order:

$$1,2,3,3,4,4,5,5,6,7$$

The $$5$$th and $$6$$th scores are both $$4$$.

So, the median of group A is:

$$4$$ Group B has $$12$$ players, so the median is the average of the $$6$$th and $$7$$th scores.

List group B in order:

$$2,3,4,4,5,5,5,6,6,7,7,8$$

The $$6$$th and $$7$$th scores are both $$5$$.

So, the median of group B is: $$5$$

The difference is:

$$5-4=1$$

Final answer: $$1$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f05k0y0mjg8wvx4oi6dh","texte_question":"

The prices, in dollars, of gasoline at five stations are:

$$3.589,3.629,3.609,3.649,3.689$$

What is the median price?

","type_question":"QCM","explication":"

Put the prices in order from least to greatest:

$$3.589,3.609,3.629,3.649,3.689$$

There are $$5$$ prices, so the median is the middle value.

The middle value is the $$3$$rd value.

The $$3$$rd value is: $$3.629$$

Final answer: $$3.629$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$3.609$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$3.629$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$3.649$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$3.689$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f05m0y0sjg8w1h4sg36g","texte_question":"

A frequency table summarizes weights of $$60$$ animals. A new value of $$100$$ pounds is added, creating a data set of $$61$$ animals. Which statement must be true?

","type_question":"QCM","explication":"

A value of $$100$$ pounds is added to a data set of animal weights.

Since $$100$$ pounds is greater than the original mean, the mean increases.

The original data set had $$60$$ values, so the original median was based on the $$30$$th and $$31$$st values.

After adding a large value, the new data set has $$61$$ values, so the median is the $$31$$st value.

Because the added value is at the high end, the middle position does not move lower.

In this case, the statement that must be true is that the mean increases and the median stays the same.

Final answer: The mean increases and the median stays the same.

","points":1,"temps_limite":60,"reponses":[{"texte":"The mean increases and the median increases","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"The mean increases and the median stays the same","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"The mean decreases and the median increases","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

The mean decreases and the median stays the same

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f05o0y0yjg8whkbqooxo","texte_question":"

Two teams each have $$8$$ runners. The mean time for Team A is $$4.2$$ minutes, and the mean time for Team B is $$4.8$$ minutes. Which must be true?

I. Every runner on Team A ran faster than every runner on Team B.

II. The median time of Team B is greater than the median time of Team A.

III. At least one runner on Team B ran slower than some runner on Team A.

","type_question":"QCM","explication":"

The mean time for Team B is greater than the mean time for Team A.

Since larger time means slower running, Team B was slower on average.

Statement I does not have to be true because averages do not prove that every runner on one team was faster than every runner on the other team.

Statement II does not have to be true because the mean does not always determine the median.

Statement III must be true.

If no runner on Team B ran slower than any runner on Team A, then every Team B time would be less than or equal to every Team A time.

That would make Team B have a mean less than or equal to Team A, which contradicts the fact that Team B has a greater mean.

So, at least one runner on Team B must have run slower than some runner on Team A.

Final answer: III only

","points":1,"temps_limite":60,"reponses":[{"texte":"III only","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"I and III only","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"II and III only","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

I, II, and III

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f05r0y14jg8wnaxiscpm","texte_question":"

The mean number of hours worked by $$15$$ employees is $$32$$ hours. After one employee leaves, the mean of the remaining $$14$$ employees is $$30$$ hours. How many hours did the employee who left work?

","type_question":"QCM","explication":"

Find the original total number of hours.

$$15\\cdot32=480$$

Find the total number of hours after one employee leaves.

$$14\\cdot30=420$$

The number of hours worked by the employee who left is the difference:

$$480-420=60$$

Final answer: $$60$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$60$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$62$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$64$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$70$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f05v0y1ajg8w4r5rf32r","texte_question":"

The mean score of $$9$$ players is $$18$$ points. When the highest score is removed, the mean of the remaining $$8$$ players is $$16$$ points. What was the highest score?

","type_question":"QCM","explication":"

Find the total score of all $$9$$ players.

$$9\\cdot18=162$$

Find the total score of the remaining $$8$$ players.

$$8\\cdot16=128$$

The highest score is the difference:

$$162-128=34$$

Final answer: $$34$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$30$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$32$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$34$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$36$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["problem-solving-and-data-analysis-one-variable-data-distributions-and-measures-of-center-and-spread"],"date":"2026-06-04T09:04:48.680Z","modified":"2026-07-14T05:49:53.654Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L1a",null,{"targetType":"quiz","targetSlug":"psat-8-9-one-variable-data-quiz-4"}]}]]}]}]]

Quiz 4

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