fastest recorded speeds of various large wild cats (miles per hour) 70,50,30,40,35,30,30,40,15.
The standard deviation of is 14.01 and the mean is 37.7
I have created a dot plot of the data and now I need to find out within how many standard deviations of the mean does all the data fall but I am not sure how to do this Please help
The maximum value is 70, which is
(70-37.7)/14.01=2.3 standard deviations above the mean.
You can calculate similarly for the smallest value of 15.
To find out how many standard deviations all the data falls within the mean, you can use the concept of z-scores. A z-score measures how many standard deviations an individual data point is from the mean.
To calculate the z-score for each data point, you can use the formula:
z = (x - μ) / σ
where z is the z-score, x is the data point, μ is the mean, and σ is the standard deviation.
Let's calculate the z-score for each data point using the given mean of 37.7 and standard deviation of 14.01:
For 70: z = (70 - 37.7) / 14.01 = 2.3
For 50: z = (50 - 37.7) / 14.01 = 0.88
For 30: z = (30 - 37.7) / 14.01 = -0.55
For 40: z = (40 - 37.7) / 14.01 = 0.16
For 35: z = (35 - 37.7) / 14.01 = -0.19
For 30: z = (30 - 37.7) / 14.01 = -0.55
For 30: z = (30 - 37.7) / 14.01 = -0.55
For 40: z = (40 - 37.7) / 14.01 = 0.16
For 15: z = (15 - 37.7) / 14.01 = -1.62
Now, to determine how many standard deviations each data point is from the mean, we compare the absolute value of their respective z-scores. If the absolute value of the z-score is less than or equal to 1, it falls within 1 standard deviation. If it's less than or equal to 2, it falls within 2 standard deviations, and so on.
Based on the calculated z-scores, here's the number of standard deviations each data point falls from the mean:
70: 2.3 (more than 2 standard deviations from the mean)
50: 0.88 (within 1 standard deviation)
30: -0.55 (within 1 standard deviation)
40: 0.16 (within 1 standard deviation)
35: -0.19 (within 1 standard deviation)
30: -0.55 (within 1 standard deviation)
30: -0.55 (within 1 standard deviation)
40: 0.16 (within 1 standard deviation)
15: -1.62 (within 2 standard deviations)
Now, to determine within how many standard deviations all the data falls from the mean, we consider the maximum absolute value of the z-scores, which in this case is 2.3.
Therefore, all the data falls within 2.3 standard deviations of the mean.