Math

QuestionFind the five-number summary (min, Q1, median, Q3, max) for the dataset: 53, 18, 54, 65, 48, 70, 38, 63, 28, 41, 45, 33, 52, 20, 43, 23, 30, 79, 42, 89.

Studdy Solution

STEP 1

Assumptions1. The data set is given in the table. . The five-number summary includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
3. The data set is not sorted in ascending order.

STEP 2

First, we need to sort the data set in ascending order.

STEP 3

Sort the data set in ascending order.
18,20,23,28,30,33,38,41,42,43,45,48,52,53,54,63,65,70,79,8918,20,23,28,30,33,38,41,42,43,45,48,52,53,54,63,65,70,79,89

STEP 4

Now, we can find the minimum and maximum of the data set. The minimum is the first number in the sorted list and the maximum is the last number.

STEP 5

Find the minimum and maximum of the data set.
Minimum=18Minimum =18Maximum=89Maximum =89

STEP 6

Next, we need to find the median of the data set. The median is the middle number when the data set is sorted in ascending order. If the data set has an odd number of observations, the median is the middle number. If the data set has an even number of observations, the median is the average of the two middle numbers.

STEP 7

Since our data set has20 observations (an even number), the median is the average of the10th and11th observations.
Median=(41+42)/2Median = (41 +42)/2

STEP 8

Calculate the median.
Median=(41+42)/2=41.5Median = (41 +42)/2 =41.5

STEP 9

Next, we need to find the first quartile (Q) and the third quartile (Q3). Q is the median of the lower half of the data (not including the median if the number of observations is odd), and Q3 is the median of the upper half of the data.

STEP 10

To find Q, we take the median of the first10 numbers.
Q=(30+33)/2Q = (30 +33)/2

STEP 11

Calculate Q.
Q=(30+33)/=31.5Q = (30 +33)/ =31.5

STEP 12

To find Q, we take the median of the last10 numbers.
Q=(54+63)/2Q = (54 +63)/2

STEP 13

Calculate Q3.
Q3=(54+63)/2=58.5Q3 = (54 +63)/2 =58.5The five-number summary for the data set isMinimum =18Q=31.5Q_{}=31.5Median =41.5Q3=58.5Q_{3}=58.5Maximum =89

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