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Using Algebra in Statistics and Probability Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to Using Algebra in Statistics and Probability Study Guide.

Using Algebra in Statistics and Probability Practice Questions

Problems

Practice 1

Find the answer to each question.

  1. The mean of a set of six values is 8. If five of the values are 4, 6, 7, 10, and 12, what is the sixth value?
  2. What value must be added to the set {–3, –2, 5, 7, 8, 8, 12} to make the mean 4?
  3. A set contains the values {10, 11, 14, 18, 20, 21}. A seventh value is added. What values could be added to the set without changing the median of the set to either 14 or 18?
  4. What values could be added to the set {2, 6, 6, 6, 12, 15} to make the range 15?

Practice 2

  1. A deck of cards contains 7 hearts, 9 spades, 11 clubs, and an unknown number of diamonds. If the probability of selecting a spade is , how many diamonds are in the deck?
  2. A sack contains 4 baseballs, 5 golf balls, and 6 tennis balls. How many baseballs must be added to the sack to make the probability of selecting a baseball ?
  3. A jar holds 14 pennies, 16 nickels, 6 dimes, and 12 quarters. How many nickels must be removed from the jar to make the probability of selecting a nickel ?

Solutions

Practice 1

1. The mean of a set is equal to the sum of the values divided by the number of values. Let x represent the sixth value in the set:
4 + 6 + 7 + 10 + 12 + x = 39 + x
39 + x = 48
x = 9
The sixth value of the set is 9.
2. The mean of a set is equal to the sum of the values divided by the number of values. The set contains seven values, so let x represent the eighth value:
–3 + –2 + 5 + 7 + 8 + 8 + 12 + x = 35 + x
35 + x = 32
x = –3
The eighth value of the set is –3.
3. The median value of a set is the middle value of the set after the values have been ordered from least to greatest. The set {10, 11, 14, 18, 20, 21} has an even number of values, so the median is the average of the two middle values, 14 and 18. 14 + 18 = 32, and 32 ÷ 2 = 16. The median of the set is 16. When a new value is added to the set, there will be an odd number of values in the set, and after the values are ordered, the median will be the fourth value. If the number is 14 or less, 14 will become the median. If the median is 18 or greater, 18 will become the median. The only values that could be added without the median becoming 14 or 18 are values that are between 14 and 18. If x is the new value, then 14 < x < 18.
4. The range of a data set is the difference between its greatest value and its least value. In the set {2, 6, 6, 6, 12, 15}, the greatest value is 15 and the least value is 2. For the range to change, the new value must be either less than 2 or greater than 15. Let x represent the new value in the set. Because the new range is 15, either 15 – x = 15 or x – 2 = 15:
15 – x = 15    x – 2 = 15
x = 0       x = 17
x = 0
The new value is either 0 or 17.
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