The diameters of circles (in mm) drawn in a design are given below
Diameters | No. of children |
33-36 | 15 |
37-40 | 17 |
41-44 | 21 |
45-48 | 22 |
49-52 | 25 |
Class Interval | Frequency \(f_i\) | \(mid-point\,x_i\) | \(y_i=\frac{x_i-42.5}{4}\) | \(f_i^2\) | \(f_iy_i\) | \(f_iy_1^2\) |
32.5-36.5 | 15 | 34.5 | -2 | 4 | -30 | 60 |
36.5-40.5 | 17 | 38.5 | -1 | 1 | -17 | 17 |
40.5-44.5 | 21 | 42.5 | 0 | 0 | 0 | 0 |
44.5-48.5 | 22 | 46.5 | 1 | 1 | 22 | 22 |
48.5-52.5 | 25 | 50.5 | 2 | 4 | 50 | 100 |
100 | 25 | 199 |
Here, N = 100, h = 4
Let the assumed mean, A, be 42.5
Mean, \(\bar{x}=A\frac{\sum_{i=1}^5f_ix_i}{n}×h=42.5+\frac{25}{100}×4=43.5\)
Variance (σ2) = \(\frac{h^2}{N^2}[N\sum_{i=1}^5f_iy_i^2-(\sum_{i=1}^5f_iy_i)^2]\)
\(=\frac{16}{10000}[100×199-(25)^2]\)
\(=\frac{16}{10000}[19900-625]\)
\(=\frac{16}{1000}×19275\)
\(=30.84\)
\(Standard\,\,deviation\.(σ) =5.55\)
What inference do you draw about the behaviour of Ag+ and Cu2+ from these reactions?
According to layman’s words, the variance is a measure of how far a set of data are dispersed out from their mean or average value. It is denoted as ‘σ2’.
Read More: Difference Between Variance and Standard Deviation
The spread of statistical data is measured by the standard deviation. Distribution measures the deviation of data from its mean or average position. The degree of dispersion is computed by the method of estimating the deviation of data points. It is denoted by the symbol, ‘σ’.
1. Population Standard Deviation
2. Sample Standard Deviation