# From the prices of shares of X and Y below, find out which is more stable in value:

x 35 54 52 53 56 58 52 50 51 49

y 108 107 105 105 106 107 104 103 104 101

**Solution:**

The prices of the shares X are

35, 54, 52, 53, 56, 58, 52, 50, 51, 49

Here, the number of observations, N = 10

Mean,

x = 1/N ∑^{10}_{i = 1}x_{i}

= 1/10 x 510

= 51

The following table is obtained corresponding to shares X.

x_{i} |
(x_{i} - x) |
(x_{i} - x)^{2} |

35 | -16 | 256 |

54 | 3 | 9 |

52 | 1 | 1 |

53 | 2 | 4 |

56 | 5 | 25 |

58 | 7 | 49 |

52 | 1 | 1 |

50 | - 1 | 1 |

51 | 0 | 0 |

49 | - 2 | 4 |

350 |

(σ_{1}²) = 1/N [N ∑^{10}_{i = 1}(x_{i} - x)

= 1/10 × 350

= 35

(σ_{1}) = √35

= 5.91

C.V.(Shares X) = σ_{1}/X × 100

= 5.91/51 × 100

= 11.58

The prices of the shares Y are

108, 107, 105, 105, 106, 107, 104, 103, 104, 101

Here, the number of observations, N = 10

Mean

y = 1/N ∑^{10}_{i = 1}y_{i}

= 1/10 x 1050

= 105

The following table is obtained corresponding to shares Y.

y_{i} |
(y_{i} - y) |
(y_{i} - y)² |

108 | 3 | 9 |

107 | 2 | 4 |

105 | 0 | 0 |

105 | 0 | 0 |

106 | 1 | 1 |

107 | 2 | 4 |

104 | - 1 | 1 |

103 | - 2 | 4 |

104 | - 1 | 1 |

101 | - 4 | 16 |

40 |

Variance,

(σ_{2}²) = 1/N [N ∑^{10}_{i = 1}(y_{i} - y)

= 1/10 × 40

= 4

Standard deviation,

(σ_{2}) = √4

= 2

C.V.(Shares X) = σ_{2}/X × 100

= 2/105 × 100

= 1.9

C.V. of prices of shares X is greater than the C.V of prices of shares Y.

Thus, the prices of shares Y are more stable than the prices of shares X

NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.3 Question 2

## From the prices of shares of X and Y below, find out which is more stable in value:

**Summary:**

From the given data, the prices of shares Y are more stable than the prices of shares X