Math

QuestionAnalyze earnings of famous deceased individuals. Calculate mean, median, mode, midrange, and comment on skewness. Data in millions: Yves Saint Laurent 350, Charles Schulz 35, Rodgers & Hammerstein 235, John Lennon 15, Michael Jackson 90, Dr. Seuss 15, Elvis Presley 55, Albert Einstein 10, JRR Tolkien 50, Jimi Hendrix 8.

Studdy Solution

STEP 1

Assumptions1. The earnings of each celebrity are given in millions of dollars. . The data is not grouped.
3. We are asked to find the mean, median, mode, and midrange of the data.
4. We are also asked to comment on the skewness of the data.

STEP 2

First, let's list all the data points in ascending order.
810151535505590235350\begin{array}{cccccccccccc}8 &10 &15 &15 &35 &50 &55 &90 &235 &350\end{array}

STEP 3

To find the mean, we add all the data points and divide by the number of data points.
Mean=i=1nxinMean = \frac{\sum_{i=1}^{n} x_i}{n}

STEP 4

Plug in the values for each data point and the total number of data points to calculate the mean.
Mean=8+10+15+15+35+50+55+90+235+35010Mean = \frac{8 +10 +15 +15 +35 +50 +55 +90 +235 +350}{10}

STEP 5

Calculate the mean.
Mean=86310=86.3Mean = \frac{863}{10} =86.3

STEP 6

To find the median, we need to find the middle value of the data set. Since there are10 data points, the median is the average of the5th and6th data points.
Median=5thdatapoint+6thdatapoint2Median = \frac{5th\, data\, point +6th\, data\, point}{2}

STEP 7

Plug in the values for the5th and6th data points to calculate the median.
Median=35+502Median = \frac{35 +50}{2}

STEP 8

Calculate the median.
Median=852=42.5Median = \frac{85}{2} =42.5

STEP 9

The mode is the data point that appears most frequently. In this case, the value15 appears twice, so it is the mode.
Mode=15Mode =15

STEP 10

The midrange is the average of the smallest and largest data points.
Midrange=Smallestdatapoint+Largestdatapoint2Midrange = \frac{Smallest\, data\, point + Largest\, data\, point}{2}

STEP 11

Plug in the values for the smallest and largest data points to calculate the midrange.
Midrange=8+350Midrange = \frac{8 +350}{}

STEP 12

Calculate the midrange.
Midrange=3582=179Midrange = \frac{358}{2} =179

STEP 13

To comment on the skewness, we compare the mean and the median. If the mean is greater than the median, the data is positively skewed. If the mean is less than the median, the data is negatively skewed. If the mean is equal to the median, the data is symmetric. In this case, the mean (86.3) is greater than the median (42.5), so the data is positively skewed.
The mean is 86.3million,themedianis86.3 million, the median is 42.5 million, the mode is 15million,andthemidrangeis15 million, and the midrange is 179 million. The data is positively skewed.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord