Math  /  Data & Statistics

QuestionFind the median for the data items in the given frequency distribution. \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline Score, x\mathbf{x} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline Frequency, f\mathbf{f} & 3 & 4 & 2 & 6 & 1 & 1 & 1 & 2 \\ \hline \end{tabular}
The median is \square . (Type an integer or a decimal.)

Studdy Solution

STEP 1

1. The scores are discrete values from 1 to 8.
2. The frequency distribution provides the number of occurrences for each score.
3. The median is the value separating the higher half from the lower half of the data set.

STEP 2

1. Calculate the total number of data points.
2. Determine the cumulative frequency for each score.
3. Identify the median class or score.

STEP 3

Calculate the total number of data points by summing the frequencies:
3+4+2+6+1+1+1+2=203 + 4 + 2 + 6 + 1 + 1 + 1 + 2 = 20

STEP 4

Calculate the cumulative frequency for each score:
- Cumulative frequency for score 1: 33 - Cumulative frequency for score 2: 3+4=73 + 4 = 7 - Cumulative frequency for score 3: 7+2=97 + 2 = 9 - Cumulative frequency for score 4: 9+6=159 + 6 = 15 - Cumulative frequency for score 5: 15+1=1615 + 1 = 16 - Cumulative frequency for score 6: 16+1=1716 + 1 = 17 - Cumulative frequency for score 7: 17+1=1817 + 1 = 18 - Cumulative frequency for score 8: 18+2=2018 + 2 = 20

STEP 5

Identify the median class or score. Since there are 20 data points, the median is the average of the 10th and 11th data points.
From the cumulative frequencies: - The 10th data point is in the score 4 class (as cumulative frequency reaches 15 at score 4). - The 11th data point is also in the score 4 class.
Thus, the median score is:
4 \boxed{4}
The median is:
4 \boxed{4}

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