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Calculate the mean and median of each data set, and determine what type of distribution it has.

[tex]\[
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline
\text{Data Set 1} & 5 & 8 & 9 & 6 & 3 & 2 & 10 & 8 & 5 & 4 & 3 \\
\hline
\text{Data Set 2} & 8 & 7 & 3 & 2 & 4 & 6 & 2 & 7 & 4 & 9 & 6 \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnswer
### Step-by-Step Solution

To calculate the mean and median of each dataset, follow these steps:

#### Data Set 1: [5, 8, 9, 6, 3, 2, 10, 8, 5, 4, 3]

1. Calculate the Mean:
- Sum all the values in the data set:
[tex]\( 5 + 8 + 9 + 6 + 3 + 2 + 10 + 8 + 5 + 4 + 3 = 63 \)[/tex]
- Count the total number of values: [tex]\( 11 \)[/tex]
- Divide the sum by the number of values to get the mean:
[tex]\[ \text{Mean}_1 = \frac{63}{11} \approx 5.7273 \][/tex]

2. Calculate the Median:
- Sort the data set in ascending order:
[tex]\[ [2, 3, 3, 4, 5, 5, 6, 8, 8, 9, 10] \][/tex]
- Identify the middle value (since there are 11 values, the median is the 6th value in the sorted list):
[tex]\[ \text{Median}_1 = 5 \][/tex]

#### Data Set 2: [8, 7, 3, 2, 4, 6, 2, 7, 4, 9, 6]

1. Calculate the Mean:
- Sum all the values in the data set:
[tex]\( 8 + 7 + 3 + 2 + 4 + 6 + 2 + 7 + 4 + 9 + 6 = 58 \)[/tex]
- Count the total number of values: [tex]\( 11 \)[/tex]
- Divide the sum by the number of values to get the mean:
[tex]\[ \text{Mean}_2 = \frac{58}{11} \approx 5.2727 \][/tex]

2. Calculate the Median:
- Sort the data set in ascending order:
[tex]\[ [2, 2, 3, 4, 4, 6, 6, 7, 7, 8, 9] \][/tex]
- Identify the middle value (since there are 11 values, the median is the 6th value in the sorted list):
[tex]\[ \text{Median}_2 = 6 \][/tex]

### Summary of Results:

- Data Set 1:
- Mean: [tex]\( \approx 5.7273 \)[/tex]
- Median: [tex]\( 5 \)[/tex]

- Data Set 2:
- Mean: [tex]\( \approx 5.2727 \)[/tex]
- Median: [tex]\( 6 \)[/tex]

#### Distribution Type:
To determine the type of distribution, compare the mean and median:
- For Data Set 1, the mean (5.7273) is higher than the median (5). This typically suggests a positive skew (right-skewed distribution).
- For Data Set 2, the mean (5.2727) is slightly lower than the median (6). This typically suggests a negative skew (left-skewed distribution).

#### Labels for Each Data Set:
- Data Set 1:
- Mean: 5.7273
- Median: 5
- Distribution: Positive skew

- Data Set 2:
- Mean: 5.2727
- Median: 6
- Distribution: Negative skew
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