Studdy AI Logo
Math

QuestionFind the mean, median, and mode of the data set: 45.4, 75.2, 38.8, 56.6, 40.4, 75.2, 62.9, 75.2, 53.1, 59.8. Round to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The data set is given as follows45.475.38.856.640.4\begin{array}{lllll}45.4 &75. &38.8 &56.6 &40.4\end{array} 75.62.975.53.159.8\begin{array}{lllll}75. &62.9 &75. &53.1 &59.8\end{array} . We need to find the arithmetic mean, median, and mode of this data set.
3. The arithmetic mean is the sum of all numbers divided by the count of numbers.
4. The median is the middle number when the numbers are arranged in ascending order. If there are two middle numbers, the median is the average of those two numbers.
5. The mode is the number that appears most frequently in the data set.

STEP 2

First, we need to find the sum of all numbers in the data set.Sum=45.4+75.2+38.8+56.6+40.4+75.2+62.9+75.2+53.1+59.8Sum =45.4 +75.2 +38.8 +56.6 +40.4 +75.2 +62.9 +75.2 +53.1 +59.8

STEP 3

Calculate the sum.
Sum=582.6Sum =582.6

STEP 4

Now, let's find the count of numbers in the data set. There are10 numbers in the data set.

STEP 5

We can now calculate the arithmetic mean by dividing the sum by the count of numbers.
Arithmetic mean=Sum/Count of numbersArithmetic\, mean = Sum / Count\, of\, numbers

STEP 6

Plug in the values for the sum and the count of numbers to calculate the arithmetic mean.
Arithmetic mean=582.6/10Arithmetic\, mean =582.6 /10

STEP 7

Calculate the arithmetic mean.
Arithmetic mean=582.6/10=58.26Arithmetic\, mean =582.6 /10 =58.26

STEP 8

Next, let's find the median. First, we need to arrange the numbers in ascending order.

STEP 9

The numbers in ascending order are38.840.445.453.56.6\begin{array}{lllll}38.8 &40.4 &45.4 &53. &56.6\end{array} 59.862.975.275.275.2\begin{array}{lllll}59.8 &62.9 &75.2 &75.2 &75.2\end{array}

STEP 10

The median is the middle number. Since there are10 numbers, the median is the average of the5th and6th numbers.
Median=(56.6+59.8)/2Median = (56.6 +59.8) /2

STEP 11

Calculate the median.
Median=(56.6+59.8)/=58.Median = (56.6 +59.8) / =58.

STEP 12

Finally, let's find the mode. The mode is the number that appears most frequently in the data set.

STEP 13

The number75.2 appears three times in the data set, which is more than any other number. Therefore, the mode is75.2.
The arithmetic mean of the data set is58.26, the median is58.2, and the mode is75.2.

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