Find the observation with lowest frequency in 4, 5, 7, 4, 8, 5, 4, 8, 5, 4 .

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Solution

Given data: 4, 5, 7, 4, 8, 5, 4, 8, 5, 4.
Arranging the given data in ascending order: 4, 4, 4, 4, 5, 5, 5, 7, 8, 8. $[1 m a r k]$
We can see that 4 is repeated 4 times, 5 is repeated thrice, 7 once and 8 is repeated twice.
Thus, the observation with lowest frequency is 7. $[1 m a r k]$

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A shopkeeper sold shoes of the following sizes in a day. Prepare a table using tally marks. $7, 5, 4, 4, 6, 8, 4, 4, 7, 8, 5, 7, 5, 8, 6, 4, 8, 4, 6, 7, 7, 5, 5, 4, 5, 4, 7, 7, 6, 6, 5, 4, 4, 6, 5, 6, 7, 8, 7, 4$

$Name the multiplication property of rational numbers shown below: (i) \frac{3}{5} \times \frac{- 8}{9} = \frac{- 8}{9} \times \frac{3}{5} (i i) \frac{- 3}{4} \times (\frac{5}{7} \times \frac{- 8}{15}) = (\frac{- 3}{5} \times \frac{5}{7}) \times \frac{- 8}{15} (i i i) \frac{4}{5} \times (\frac{3}{- 8} + \frac{- 4}{7}) = \frac{4}{5} \times \frac{3}{- 8} + \frac{4}{5} \times \frac{- 4}{7} (i v) \frac{- 7}{5} \times \frac{5}{- 7} = 1 (v) \frac{8}{- 9} \times 1 = 1 \times \frac{8}{- 9} = \frac{8}{- 9} (v i) \frac{- 3}{4} \times 0 = 0$

Fill in the blanks:

$(i) - 4 \times \frac{7}{9} = \frac{7}{9} \times$ ___

$(i i) \frac{5}{11} \times \frac{- 3}{8} = \frac{- 3}{8} \times$ ___

$(i i i) \frac{1}{2} \times (\frac{3}{4} + \frac{- 5}{12}) = \frac{1}{2} \times$ ____ $+ (\times) \frac{- 5}{12}$

$(i v) \frac{- 4}{5} \times \frac{5}{7} \times$ ___ $= (\frac{- 4}{5} \times \frac{5}{7}) \times \frac{- 8}{9}$

Q. Find the value of:

(1) 3⁶
(2) 6³
(3) 2⁶
(4) 1⁸
(5) 5⁴
(6) 4³
(7) 10⁵
(8) 10⁷
(9) 7⁴
(10) 8²

Q. The following data gives the marks of 20 students in Mathematics (X) and statistics (Y), each out of 10, expressed as (x, y). Construct an ungrouped frequency distribution, considering single numbers as a class:

(2, 7), (3, 8), (4, 9), (2, 8), (5, 6), (5, 7), (4, 9), (3, 8), (4, 8), (2, 9), (3, 8), (4, 8), (5, 6), (4, 7),

(4, 7), (4, 6), (5, 6), (5, 7), (4, 6), (5, 5).

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Find the observation with lowest frequency in 4, 5, 7, 4, 8, 5, 4, 8, 5, 4 .

Given data: 4, 5, 7, 4, 8, 5, 4, 8, 5, 4. Arranging the given data in ascending order: 4, 4, 4, 4, 5, 5, 5, 7, 8, 8. [1 mark] We can see that 4 is repeated 4 times, 5 is repeated thrice, 7 once and 8 is repeated twice. Thus, the observation with lowest frequency is 7. [1 mark]

Given data: 4, 5, 7, 4, 8, 5, 4, 8, 5, 4.
Arranging the given data in ascending order: 4, 4, 4, 4, 5, 5, 5, 7, 8, 8. $[1 m a r k]$
We can see that 4 is repeated 4 times, 5 is repeated thrice, 7 once and 8 is repeated twice.
Thus, the observation with lowest frequency is 7. $[1 m a r k]$