Math

QuestionFind the five number summary, range, and interquartile range from the given stem & leaf plot data.

Studdy Solution

STEP 1

Assumptions1. The stem and leaf plot represents the data set. . The key "1 |0 =10" means that a stem of1 and a leaf of0 represents the number10.

STEP 2

First, we need to convert the stem and leaf plot into a list of numbers. This is done by combining each stem with each of its leaves.

STEP 3

The list of numbers from the stem and leaf plot is10,12,21,22,24,29,29,42,42,45,49,50,52,53,57,58,59,60,6610,12,21,22,24,29,29,42,42,45,49,50,52,53,57,58,59,60,66

STEP 4

Now, we can find the five number summary. The five number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

STEP 5

The minimum is the smallest number in the list.
Min=10Min =10

STEP 6

The maximum is the largest number in the list.
Max=66Max =66

STEP 7

The median is the middle number when the numbers are arranged in ascending order. If there is an even number of numbers, the median is the average of the two middle numbers.
Med=45Med =45

STEP 8

The first quartile, Q1, is the median of the lower half of the numbers (not including the median if there are an odd number of numbers).Q1=22Q1 =22

STEP 9

The third quartile, Q3, is the median of the upper half of the numbers (not including the median if there are an odd number of numbers).
Q3=58Q3 =58

STEP 10

The range is the difference between the maximum and minimum.
Range=MaxMinRange = Max - Min

STEP 11

Plug in the values for the maximum and minimum to calculate the range.
Range=6610Range =66 -10

STEP 12

Calculate the range.
Range=6610=56Range =66 -10 =56

STEP 13

The interquartile range is the difference between Q3 and Q.
InterquartileRange=Q3QInterquartile\, Range = Q3 - Q

STEP 14

Plug in the values for Q3 and Q to calculate the interquartile range.
InterquartileRange=5822Interquartile\, Range =58 -22

STEP 15

Calculate the interquartile range.
InterquartileRange=5822=36Interquartile\, Range =58 -22 =36The five number summary is Min =10, Q =22, Med =45, Q3 =58, Max =66. The range is56 and the interquartile range is36.

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