Question

the plot shows the temperatures (in °f) for a group of children who visited a doctors office. what conclusions can be drawn from the data set? check all that apply. the measures of center are the same. the interquartile range is 4. there is little variability in the data. the average temperature is 98. the data is clustered around the mean.

Explanation:

Step1: Calculate measures of center

To find the mean, sum all values weighted by frequency and divide by total number of data - points. Median is the middle - value when data is ordered. Mode is the most frequent value. From the dot - plot, we can see that the data is not symmetric, so measures of center are not the same.

Step2: Calculate inter - quartile range

First, find the first quartile ($Q_1$) and third quartile ($Q_3$). The inter - quartile range $IQR = Q_3−Q_1$. From the dot - plot, if we order the data, $Q_1 = 97$, $Q_3 = 99$, so $IQR=99 - 97=2
eq4$.

Step3: Analyze variability

The data ranges from 96 to 100. Since the range is $100 - 96 = 4$ and the data is somewhat spread out, there is not little variability.

Step4: Calculate average (mean)

Sum of all data points: $(96\times1)+(97\times2)+(98\times4)+(99\times2)+(100\times1)=96 + 194+392+198+100 = 980$. There are $1 + 2+4+2 + 1=10$ data points. Mean $=\frac{980}{10}=98$.

Step5: Check data clustering

The data has more points around 98, so it is clustered around the mean.

Answer:

The average temperature is 98.
The data is clustered around the mean.