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Find the median of each of the following scores

x If | Cumulative Frequency
|--|--
300-309 | 9 | 9
310-319 | 20 | 29
320-329 | 24 | 53
330-339 | 38 | 91
340-349 | 48 | 139
350-359 | 27 | 166
360-369 | 17 | 183
370-379 | 6 | 189


User Karimi
by
8.6k points

1 Answer

2 votes

Answer:

332.88

Explanation:

To find the median of this data set, we first need to determine the total number of observations. This is given by the last cumulative frequency, which is 189.

Since the total number of observations is an odd number, we can find the median by identifying the middle value. The middle value is the observation that has half the data below it and half the data above it.

To find this value, we can divide the total number of observations by 2:

189 ÷ 2 = 94.5

This means that the median observation falls in the 330-339 range, since the cumulative frequency at the end of this range is 38, which is the smallest cumulative frequency greater than 94.5.

To find the exact median value, we can use the following formula:

Median = L + ((N/2 - CF) / f)

where:

L = lower limit of the median class (in this case, 330)

N = total number of observations (in this case, 189)

CF = cumulative frequency of the class preceding the median class (in this case, 20)

f = frequency of the median class (in this case, 24)

Plugging in the values, we get:

Median = 330 + ((94.5 - 20) / 24)

= 330 + (74.5 / 24)

≈ 332.88

Therefore, the median of the given scores is approximately 332.88.

User Avnish Tiwary
by
8.2k points
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