Question

choosing a measure of center
create a dot plot of the data shown below.
20, 21, 21, 25, 20, 23, 27, 23, 24, 25, 28, 24, 23, 22, 24
which measure of center would best describe a typical
value of the data set? why?
would be best,
because the data distribution is

click or tap the number line to add a dot.
20 21 22 23 24 25 26 27 28 29

Explanation:

Step1: Organize Data

List the data: 20, 21, 21, 25, 20, 23, 27, 23, 24, 25, 28, 24, 23, 22, 24. Count frequencies:

• 20: 2 times
• 21: 2 times
• 22: 1 time
• 23: 3 times
• 24: 3 times
• 25: 2 times
• 27: 1 time
• 28: 1 time

Step2: Analyze Distribution

Check if data is symmetric (no extreme skewness, outliers? 27,28 are not extreme relative to range 20 - 28). The frequencies are balanced around the middle (23 - 24). So distribution is approximately symmetric.

Step3: Choose Measure of Center

For symmetric data, mean is best (or median, but mean is preferred for symmetric). Alternatively, median also works, but since no strong skew, mean/median. Let's confirm:

• Mean: Sum all values. Sum = \(20\times2 + 21\times2 + 22 + 23\times3 + 24\times3 + 25\times2 + 27 + 28\)

= \(40 + 42 + 22 + 69 + 72 + 50 + 27 + 28\) = \(40+42=82; 82+22=104; 104+69=173; 173+72=245; 245+50=295; 295+27=322; 322+28=350\). Number of data points: 15. Mean = \(350/15 \approx 23.33\).

• Median: Middle value (8th term). Ordered data: 20,20,21,21,22,23,23,23,24,24,24,25,25,27,28. 8th term is 23.

Since distribution is symmetric (no skew), mean (or median) is best. Let's check symmetry: frequencies around 23 - 24 are similar (23:3, 24:3; 20:2,25:2; 21:2, 22:1,27:1,28:1 – slight asymmetry but not skewed). So median or mean. Typically, for symmetric, mean is used.

Answer:

Mean (or Median) would be best, because the data distribution is approximately symmetric (or nearly symmetric with no strong skewness).

(Note: If we check the dot plot, after plotting, the dots are spread with a peak around 23 - 24, and symmetric left-right. So median or mean is appropriate. For middle school, median might be simpler, but mean works too. Let's recheck ordered data: 20,20,21,21,22,23,23,23,24,24,24,25,25,27,28. The median is 23, mean ~23.33. So either is correct. The key is the distribution is symmetric (or approximately so), so mean/median is best.)

Final Answer (common choice for symmetric data):
\(\boldsymbol{\text{Mean (or Median)}}\) would be best, because the data distribution is \(\boldsymbol{\text{approximately symmetric}}\).