Question

evaluating a histogram
the data set 80, 84, 79, 44, 87, 73, 89, 90, 82, 89, 93, 97, 77, and 71 is graphed below.
use the histogram to answer the questions.
what type of distribution is this?
what is the mean?
what is the median?
which measure of center is the best choice for this data set?
histogram with x - axis bins: 40 - 49, 50 - 59, 60 - 69, 70 - 79, 80 - 89, 90 - 99 and y - axis from 0 to 8

Explanation:

Step1: Identify Distribution Type

The histogram has a single low - frequency bar on the left (40 - 49) and most data on the right, so it's left - skewed (negative skew).

Step2: Calculate the Mean

First, sum all data points: \(80 + 84+79 + 44+87+73+89+90+82+89+93+97+77+71\)
\(=44 + 71+73+77+79+80+82+84+87+89+89+90+93+97\)
\(44+(71 + 73)+(77 + 79)+80+82+84+87+(89 + 89)+90+93+97\)
\(=44 + 144+156+80+82+84+87+178+90+93+97\)
\(=44+144 = 188;188 + 156=344;344+80 = 424;424+82 = 506;506+84 = 590;590+87 = 677;677+178 = 855;855+90 = 945;945+93 = 1038;1038+97 = 1135\)
There are 14 data points. Mean \(=\frac{1135}{14}\approx81.07\)

Step3: Calculate the Median

Arrange data in order: 44, 71, 73, 77, 79, 80, 82, 84, 87, 89, 89, 90, 93, 97
There are 14 terms, so median is the average of the 7th and 8th terms.
7th term = 82, 8th term = 84. Median \(=\frac{82 + 84}{2}=\frac{166}{2}=83\)

Step4: Best Measure of Center

Since the data is left - skewed (has a low - value outlier 44), the median is less affected by outliers, so median is the best measure of center.

Answer:

• Distribution Type: Left - skewed (Negative Skew)
• Mean: \(\approx81.07\)
• Median: 83
• Best Measure of Center: Median