Question

temperature of children at a doctors office
what conclusions can be drawn from the data set? choose four correct answers.
the measures of center are the same.
there is little variability in the data.
the data is clustered around the mean.
the average temperature is 98.
the interquartile range is 4.

Explanation:

Step1: Analyze the data distribution

The data points are clustered around 98. The range of values is from 97 - 100 (assuming each 'X' represents a data point). The spread is not large, indicating little variability.

Step2: Check measures of center

Since the data is symmetrically distributed around 98 (clustered), the mean, median and mode (measures of center) will be approximately the same.

Step3: Calculate the inter - quartile range (IQR)

First, find the median. Let's assume the number of data points: if we count the 'X's (say \(n = 15\)). The median is the 8th value. If data is \(97,97,97,98,98,98,98,98,98,98,99,99,99,100,100\) (hypothetical count based on the plot). The first quartile \(Q_1\) (4th value) is 98, the third quartile \(Q_3\) (12th value) is 99. \(IQR=Q_3 - Q_1=99 - 98 = 1
eq4\)

Step4: Check the average

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\). If we assume values (based on the plot) \(x_1 = 97,x_2 = 97,x_3 = 97,x_4 = 98,x_5 = 98,x_6 = 98,x_7 = 98,x_8 = 98,x_9 = 98,x_{10}=98,x_{11}=99,x_{12}=99,x_{13}=99,x_{14}=100,x_{15}=100\). \(\sum_{i=1}^{15}x_i=(3\times97)+(7\times98)+(3\times99)+(2\times100)=291 + 686+297 + 200=1474\). \(\bar{x}=\frac{1474}{15}\approx98.27\approx98\) (approximate due to data - point assumption from the plot)

Answer:

The measures of center are the same, There is little variability in the data, The data is clustered around the mean, The average temperature is 98.