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Math  /  Data & Statistics

Question31,33,36,41,3431,33,36,41,34
Find the standard deviation of the data set. Round your answer to the nearest hundredth. □\square pieces of candy

Studdy Solution

STEP 1

What is this asking? We need to find how spread out these numbers are, which is what standard deviation measures. Watch out! Don't forget to take the square root at the end to get the standard deviation, and round correctly!

STEP 2

1. Calculate the mean.
2. Calculate the squared differences.
3. Calculate the variance.
4. Calculate the standard deviation.

STEP 3

Let's **add up** all the numbers: 31+33+36+41+34=17531 + 33 + 36 + 41 + 34 = 175.

STEP 4

Now, **divide** that sum by the number of values, which is **5**: 175÷5=35175 \div 5 = 35.
So, our **mean** is 3535.

STEP 5

We'll find the difference between each number and the mean of 3535, then **square** each difference.

STEP 6

For 3131: (31−35)2=(−4)2=16(31 - 35)^2 = (-4)^2 = 16. For 3333: (33−35)2=(−2)2=4(33 - 35)^2 = (-2)^2 = 4. For 3636: (36−35)2=(1)2=1(36 - 35)^2 = (1)^2 = 1. For 4141: (41−35)2=(6)2=36(41 - 35)^2 = (6)^2 = 36. For 3434: (34−35)2=(−1)2=1(34 - 35)^2 = (-1)^2 = 1.

STEP 7

Now, **add up** all those squared differences: 16+4+1+36+1=5816 + 4 + 1 + 36 + 1 = 58.

STEP 8

**Divide** that sum by the number of values, which is **5**, to get the **variance**: 58÷5=11.658 \div 5 = 11.6.

STEP 9

Finally, take the **square root** of the variance to find the **standard deviation**: 11.6≈3.405877\sqrt{11.6} \approx 3.405877.

STEP 10

Rounded to the nearest hundredth, the standard deviation is **3.41**.

STEP 11

The standard deviation of the data set, rounded to the nearest hundredth, is 3.41.

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