Question

question
based on the two data sets represented below, complete the following sentences.
data set b
data set c
answer attempt 1 out of 2
the mean of data set b is than the mean of data set c. the range of data set b is than the range of data set c.

Explanation:

Step1: Calculate the mean of Data Set B

Count the number of data points for each value in Data Set B:

• \(71\): \(3\)
• \(72\): \(1\)
• \(73\): \(3\)
• \(74\): \(4\)
• \(75\): \(1\)
• \(76\): \(5\)
• \(77\): \(4\)
• \(78\): \(4\)

The sum of the data points is \(71\times3 + 72\times1+73\times3 + 74\times4+75\times1+76\times5+77\times4+78\times4\)

$$
LATEXBLOCK0
$$

The total number of data points \(n_B=3 + 1+3 + 4+1+5+4+4=25\)
The mean of Data Set B, \(\bar{x}_B=\frac{1875}{25}=75\)

Step2: Calculate the mean of Data Set C

Count the number of data points for each value in Data Set C:

• \(69\): \(5\)
• \(70\): \(2\)
• \(71\): \(5\)
• \(72\): \(2\)
• \(73\): \(2\)
• \(74\): \(5\)
• \(75\): \(4\)

The sum of the data points is \(69\times5+70\times2 + 71\times5+72\times2+73\times2+74\times5+75\times4\)

$$
LATEXBLOCK1
$$

The total number of data points \(n_C=5 + 2+5 + 2+2+5+4=25\)
The mean of Data Set C, \(\bar{x}_C=\frac{1800}{25}=72\)

Step3: Calculate the range of Data Set B

The maximum value in Data Set B is \(78\), the minimum value is \(71\). The range of Data Set B, \(R_B=78 - 71=7\)

Step4: Calculate the range of Data Set C

The maximum value in Data Set C is \(75\), the minimum value is \(69\). The range of Data Set C, \(R_C=75 - 69 = 6\)

Answer:

The mean of Data Set B is greater than the mean of Data Set C. The range of Data Set B is greater than the range of Data Set C.