Find the mean and variance for the data:
6, 7, 10, 12, 13, 4, 8, 12
Mean = 9, Variance = 9.25
Find the mean and variance for the first \(n\) natural numbers.
Mean = \(\dfrac{n+1}{2}\), Variance = \(\dfrac{n^{2}-1}{12}\)
Find the mean and variance for the first 10 multiples of 3.
Mean = 16.5, Variance = 74.25
Find the mean and variance for the following data:
\(x_i\): 6, 10, 14, 18, 24, 28, 30
\(f_i\): 2, 4, 7, 12, 8, 4, 3
Mean = 19, Variance = 43.4
Find the mean and variance for the following data:
\(x_i\): 92, 93, 97, 98, 102, 104, 109
\(f_i\): 3, 2, 3, 2, 6, 3, 3
Mean = 100, Variance = 29.09
Find the mean and standard deviation using the short-cut method:
\(x_i\): 60, 61, 62, 63, 64, 65, 66, 67, 68
\(f_i\): 2, 1, 12, 29, 25, 12, 10, 4, 5
Mean = 64, Standard deviation = 1.69
Find the mean and variance for the following frequency distribution:
Classes: 0–30, 30–60, 60–90, 90–120, 120–150, 150–180, 180–210
Frequencies: 2, 3, 5, 10, 3, 5, 2
Mean = 107, Variance = 2276
Find the mean and variance for the following frequency distribution:
Classes: 0–10, 10–20, 20–30, 30–40, 40–50
Frequencies: 5, 8, 15, 16, 6
Mean = 27, Variance = 132
Find the mean, variance and standard deviation using the short-cut method:
Height (cm): 70–75, 75–80, 80–85, 85–90, 90–95, 95–100, 100–105, 105–110, 110–115
No. of children: 3, 4, 7, 7, 15, 9, 6, 6, 3
Mean = 93, Variance = 105.58, Standard deviation = 10.27
The diameters of circles in a design are given below. Calculate the mean and standard deviation:
Diameters (mm): 33–36, 37–40, 41–44, 45–48, 49–52
No. of circles: 15, 17, 21, 22, 25
Mean = 5.55, Standard deviation = 43.5