Question

In an experiment some people were asked to estimate the length, in cm of a piece of string. The frequency table shows their estimate.

LENGTH FREQUENCY
11 --------------- 1
12 --------------- 2
13 --------------- 4
14 --------------- 18
15 -------------- 16
16 -------------- 14
17 -------------- 20
18 -------------- 18
19 -------------- 0
20 ------------- 2
a. Find the range of their estimates
b. Find the interquartile range of their estimates

Answer 1

The range of string length estimates is 9 cm, calculated as the difference between the highest (20 cm) and lowest (11 cm) estimates. To find the interquartile range, one would need to calculate the first and third quartiles from the frequency table and subtract Q1 from Q3.

Step-by-step explanation:

The question regards the frequency table of string length estimates in an experiment. To find the range of the estimates, we need to subtract the smallest estimate from the largest one. To find the interquartile range (IQR), we need the first quartile (Q1) and the third quartile (Q3) values and then calculate IQR as Q3 - Q1.

a. The range is the difference between the highest and the lowest estimated lengths. In this case:

• Highest estimate: 20 cm
• Lowest estimate: 11 cm
• Range: 20 - 11 = 9 cm

b. To find the interquartile range (IQR), we would first need to determine the quartiles. However, finding the exact quartile values from a frequency table requires organizing the data into a chart with the corresponding cumulative frequencies. After determining the positions of Q1 and Q3 within the cumulative frequency, we would identify the corresponding string lengths for these quartiles and calculate IQR by subtracting Q1 from Q3.