The sum of two angles is 11 12 π and difference is 75 ° , find θ the angles in circular measure.

Given, Sum of two angles = 11 12 π = 11 × 180 ° 12 = 165 ° Difference of the angles = 75 ° Let the angles be x ° and y ° . So, x + y = 165 ° ⇒ x = 165 ° - y And, x - y = 75 ° ⇒ 165 ° - y - y = 75 ° ⇒ 2 y = 165 ° - 75 ° ⇒ y = 90 ° 2 = 45 ° So, x = 165 ° - 45 ° = 120 ° Thus, the value of a angle in circular measure is 180 ° = π c ∴ 120 ° = π 180 × 120 ° = 2 π 3 and 45 ° = π 180 ° × 45 ° = π 4 Hence, the measure of the angles in circular measure is 2 π 3 and π 4

Find the median of the height of the students from the following statistical data: Height (in cm ) 135 - 140 140 - 145 145 - 150 150 - 155 155 - 160 160 - 165 Number of students 7 12 20 24 20 17

Given, Class boundary-Height (in cm ) Number of students ( f ) Cumulative frequency 135 - 140 7 7 140 - 145 12 7 + 12 = 19 145 - 150 20 19 + 20 = 39 150 - 155 24 39 + 24 = 63 155 - 160 20 63 + 20 = 83 160 - 165 17 83 + 17 = 100 N = ∑ f = 100 Here, N 2 = 100 2 = 50 The cumulative frequency of the class which is just greater than 50 is 150 - 155 . Median = l + N 2 - F f m × i , where l is lower boundary of the median class, F is cumulative frequency of the class preceding the median class, f m is simple frequency of median class, i is the length of median class, N is total frequency. So, median = 150 + 50 - 20 24 × 5 = 156 . 25

Find the mode of the frequency distributive table given below: Class 16 - 18 18 - 20 20 - 22 22 - 24 24 - 26 Frequency 45 75 38 22 20

Given, Class Frequency 16 - 18 45 18 - 20 75 20 - 22 38 22 - 24 22 24 - 26 20 Here, the highest frequency is 75 and the class associated with this is 18 - 20 . So, the modal class is 18 - 20 . Mode = l + f m - f 1 2 f m - f 1 - f 2 × i , where l is lower boundary of modal class, f m is frequency of modal class, f 1 is the frequency of the class just preceding the modal class, f 2 is the frequency of the class just succeeding the modal class, i is width of the modal class. So, mode = 18 + 75 - 45 2 × 75 - 45 - 38 × 2 = 18 . 90 Hence, the required mode is 18 . 90 .