Math

QuestionFind the five-number summary (min, Q1, median, Q3, max) for the data set: 25, 53, 81, 60, 54, 46, 13, 52, 43, 39, 36, 10, 41, 37, 77, 57, 56.

Studdy Solution

STEP 1

Assumptions1. The data set is given in the table. . The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum of the data set.

STEP 2

First, we need to arrange the data in ascending order.

STEP 3

The arranged data set is as follows10,13,25,36,37,39,41,43,46,52,53,54,56,57,60,77,8110,13,25,36,37,39,41,43,46,52,53,54,56,57,60,77,81

STEP 4

The minimum value of the data set is the first number in the arranged list.
Minimum=10Minimum =10

STEP 5

The maximum value of the data set is the last number in the arranged list.
Maximum=81Maximum =81

STEP 6

The median is the middle number of the data set. Since there are17 numbers in the data set, the median is the9th number.
Median=46Median =46

STEP 7

The first quartile (Q1) is the median of the first half of the data set. Since there are numbers in the first half, the first quartile is the average of the4th and5th numbers.
Q1=(36+37)/2=36.5Q_{1} = (36+37)/2 =36.5

STEP 8

The third quartile (Q3) is the median of the second half of the data set. Since there are8 numbers in the second half, the third quartile is the average of the4th and5th numbers in the second half.
Q3=(56+57)/2=56.5Q_{3} = (56+57)/2 =56.5So, the five-number summary for the given data set isMinimum =10Q1=36.5Q_{1}=36.5Median =46Q3=56.5Q_{3}=56.5Maximum =81

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord