describe the distribution of the data with regard to the shape, outliers, center, and spread.
Time
Number of People
10 am - 11 am
20
11 am - 12 pm
21
12 pm - 1 pm
19
1 pm - 2 pm
21
2 pm - 3 pm
23
3 pm - 4 pm
19
4 pm - 5 pm
24
5 pm - 6 pm
23
6 pm - 7 pm
20
7 pm - 8 pm
23
The number of people are below the times (sorry it wouldn't let me spread it out)
Which parts of this assignment don't you understand?
I don't understand how to get the spread and center.
The spread is basically the lowest and highest numbers. The center is the median.
https://www.google.com/search?source=hp&q=statistics+spread&oq=statistics+spread&gs_l=psy-ab.3..0l4.1864.8187.0.8370.17.17.0.0.0.0.172.2075.0j17.17.0....0...1.1.64.psy-ab..0.17.2072...0i131k1.7NNQmpt8YNI
So, 24, and 19 for the spread and the center is 21?
Right.
Thank you
You're welcome.
To describe the distribution of the data, we can analyze the shape, outliers, center, and spread.
Shape: The data appears to be approximately symmetric and bell-shaped. There is no significant skewness or asymmetry evident from the provided values. The distribution follows a normal or nearly normal pattern.
Outliers: From the given data, we don't see any outliers. An outlier is a value that significantly deviates from the rest of the data points. Outliers can impact the overall shape and measures of center and spread.
Center: To determine the center of the data, we can calculate the mean (average). Adding up all the values and dividing by the total number of observations gives us the mean. In this case, we have ten values, so we sum them all and divide by ten.
Mean = (20 + 21 + 19 + 21 + 23 + 19 + 24 + 23 + 20 + 23) / 10 = 21.3
Spread: To measure the spread or variability of the data, we can calculate the range or standard deviation. The range is the difference between the highest and lowest values, and the standard deviation measures the average amount by which each value deviates from the mean.
Range = Highest Value - Lowest Value = 24 - 19 = 5
To calculate the standard deviation, we can follow these steps:
1. Calculate the difference between each value and the mean.
2. Square each difference.
3. Sum the squared differences.
4. Divide the sum by the total number of observations minus one (in this case, it's nine, since we have a sample).
5. Take the square root of the result.
Using these steps, the standard deviation for this data set can be calculated as follows:
Step 1: Calculate the differences:
(20 - 21.3) = -1.3
(21 - 21.3) = -0.3
(19 - 21.3) = -2.3
(21 - 21.3) = -0.3
(23 - 21.3) = 1.7
(19 - 21.3) = -2.3
(24 - 21.3) = 2.7
(23 - 21.3) = 1.7
(20 - 21.3) = -1.3
(23 - 21.3) = 1.7
Step 2: Square each difference:
(-1.3)^2 = 1.69
(-0.3)^2 = 0.09
(-2.3)^2 = 5.29
(-0.3)^2 = 0.09
(1.7)^2 = 2.89
(-2.3)^2 = 5.29
(2.7)^2 = 7.29
(1.7)^2 = 2.89
(-1.3)^2 = 1.69
(1.7)^2 = 2.89
Step 3: Sum the squared differences:
1.69 + 0.09 + 5.29 + 0.09 + 2.89 + 5.29 + 7.29 + 2.89 + 1.69 + 2.89 = 30.1
Step 4: Divide the sum by the total number of observations minus one:
30.1 / (10 - 1) = 3.35
Step 5: Take the square root of the result:
√3.35 ≈ 1.83
Therefore, the standard deviation of the data set is approximately 1.83.
In summary, the distribution of the data appears to be bell-shaped, with no outliers evident. The mean (center) of the data is approximately 21.3, and the range (spread) is 5. Additionally, the standard deviation (another measure of spread) is approximately 1.83.