Question

What is the five-number summary for the data set. 23, 27, 42, 45, 49, 53, 62, 71, 76, 80 Responses min: 23, Q1: 42, median: 51, Q3: 71, max: 80 min:, , 23, ,, , Q 1, :, , 42,, , median:, , 51, ,, , Q 3, :, , 71,, , max:, , 80 min: 21, Q1: 42, median: 50, Q3: 71, max: 81 min:, , 21, ,, , Q 1, :, , 42,, , median:, , 50, ,, , Q 3, :, , 71,, , max:, , 81 min: 23, Q1: 34, median: 51, Q3: 74, max: 80 min:, , 23, ,, , Q 1, : 34, ,, , median:, , 51, ,, , Q 3, :, , 74,, , max:, , 80 min: 21, Q1: 34, median: 50, Q3: 74, max: 81

Answer 1

The five - number summary for the data is : min: 23, Q1 :34, median: 51, Q3 : 74, max: 80

Using the data given for our Calculation;

• 23, 27, 42, 45, 49, 53, 62, 71, 76, 80
• n = sample size = 10

The minimum value = 23

The first quartile :

• 1/4(n+1)th term

First quartile = 1/4(11) = 2.75th term

First quartile = (27 + 42) / 2 = 34.5 ≈ 34

The median :

• 1/2(n+1)th term

Median = 1/2(11) = 5.5th term

Median = (49 + 53) / 2 = 51

The Third quartile :

• 3/4(n+1)th term

Third quartile = 3/4(11) = 8.25th term

Third quartile = (71 + 76) / 2 = 73.5 ≈ 74

Maximum : 80

Therefore, The five - number summary for the data is : min: 23, Q1 :34, median: 51, Q3 : 74, max: 80