Question

for 1 - 2, complete each statement. a community musical director is interested in comparing the ages of the members of the town’s two choirs. he displays the data in a back - to - back stem - and - leaf plot. 1. the interquartile range of good treble is than rockapella. 2. you can infer that rockapella has variability than good treble. 3. which inference can be made from comparing the two data sets? a the members of rockapella are slightly younger on average than members of good treble. b the members of good treble and rockapella are the same average age. c the members of rockapella are slightly older on average than members of good treble. d the members of good treble and rockapella are extremely different in average age. ages of choir members rockapella good treble 6, 6, 8, 8 2 0, 5, 5, 8 0, 3, 4, 4 3 2, 6, 8 1, 1, 4, 5 4 6, 6 0 5 1, 8 key: 8 | 2 = 28 key: 1 | 9 = 19

Explanation:

Step1: Write out the data sets

Rock - apella: 26, 26, 28, 28, 30, 33, 34, 34, 41, 41, 44, 45, 50
Good Treble: 19, 19, 20, 25, 25, 28, 32, 36, 38, 46, 46, 51, 58

Step2: Find the median (Q2) of each data - set

For Rock - apella (n = 13), the median (Q2) is the 7th value, so Q2 = 34.
For Good Treble (n = 13), the median (Q2) is the 7th value, so Q2 = 32.

Step3: Find Q1 and Q3 for each data - set

For Rock - apella:
The lower half is 26, 26, 28, 28, 30, 33. The median of the lower half (Q1) is $\frac{28 + 28}{2}=28$.
The upper half is 41, 41, 44, 45, 50. The median of the upper half (Q3) is 44.
The inter - quartile range (IQR) for Rock - apella is IQR = Q3 - Q1 = 44 - 28 = 16.
For Good Treble:
The lower half is 19, 19, 20, 25, 25, 28. The median of the lower half (Q1) is $\frac{20+25}{2}=22.5$.
The upper half is 36, 38, 46, 46, 51, 58. The median of the upper half (Q3) is $\frac{46 + 46}{2}=46$.
The inter - quartile range (IQR) for Good Treble is IQR = Q3 - Q1 = 46 - 22.5 = 23.5.

Step4: Compare the IQRs

Since 23.5>16, the inter - quartile range of Good Treble is greater than Rock - apella.

Step5: Analyze variability

A larger IQR indicates more variability. Since the IQR of Good Treble is larger, Rockapella has less variability than Good Treble.

Step6: Analyze average age

To estimate the average age, we can look at the medians. The median age of Rock - apella is 34 and the median age of Good Treble is 32. So the members of Rockapella are slightly older on average than members of Good Treble.

Answer:

1. greater
2. less
3. C. The members of Rockapella are slightly older on average than members of Good Treble.