QuestionCalculate the mean, median, and mode for the data set: 89, 56, 60, 48, 22, 48. Round answers to one decimal place.

Studdy Solution

STEP 1

Assumptions1. The data set is $\{89,56,60,48,22,48\}$ . The mean is the sum of all values divided by the number of values3. The median is the middle value when the data set is arranged in ascending order. If the data set has an even number of values, the median is the average of the two middle values.
4. The mode is the value that appears most frequently in the data set.

STEP 2

First, we need to find the mean. We can do this by adding all the values in the data set and then dividing by the number of values.
$Mean = \frac{Sum\, of\, all\, values}{Number\, of\, values}$

STEP 3

Now, plug in the given values to calculate the mean.
$Mean = \frac{89 +56 +60 +48 +22 +48}{6}$

STEP 4

Calculate the mean.
$Mean = \frac{89 +56 +60 +48 +22 +48}{6} =53.8$

STEP 5

Next, we need to find the median. First, arrange the data set in ascending order.
$\{22,48,48,56,60,89\}$

STEP 6

Since the number of values is even (6), the median is the average of the two middle values.
$Median = \frac{(4th\, value +3rd\, value)}{2}$

STEP 7

Now, plug in the given values to calculate the median.
$Median = \frac{56 +48}{2}$

STEP 8

Calculate the median.
$Median = \frac{56 +48}{2} =52$

STEP 9

Finally, we need to find the mode. The mode is the value that appears most frequently in the data set.
In this data set, the value48 appears twice, which is more frequent than any other value, so the mode is48.
Mean =53.8Median =52Mode =48

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