The height of 100 maize plants were measured to the nearest centimeter and the results recorded in the table below. (a) complete the table. (b) Calculate 2 d.p. (i) The mean (ii) The standard deviation. (c) Using the above plot an ogive and use it to find the 30th percentile.

Fomula ni $\bar{x} = A + \frac{\sum fd}{\sum f} \times c$.
Kutoka jedwali, $A = 42$, $\sum fd = 3$, $\sum f = 100$, na $c = 5$.

Fomula ni $s = c \sqrt{\frac{\sum fd^2}{\sum f} - \left(\frac{\sum fd}{\sum f}\right)^2}$.
Kutoka jedwali, $c = 5$, $\sum fd^2 = 235$, $\sum fd = 3$, na $\sum f = 100$.

• 25-29: 29.5, CF = 5
• 30-34: 34.5, CF = 17
• 35-39: 39.5, CF = 35
• 40-44: 44.5, CF = 65
• 45-49: 49.5, CF = 82
• 50-54: 54.5, CF = 93
• 55-59: 59.5, CF = 100 Anza ogive kwa (24.5, 0).

• Chora grafu ambapo mhimili wa x unawakilisha urefu (Height) na mhimili wa y unawakilisha masafa jumla (Cumulative Frequency).
• Panga pointi zilizoorodheshwa hapo juu na uziunganishe kwa mstari laini.

• Jumla ya masafa ni $N = 100$.
• Asilimia ya 30 inalingana na nafasi ya $0.30 \times N = 0.30 \times 100 = 30$.
• Kwenye ogive, tafuta 30 kwenye mhimili wa y (Cumulative Frequency).
• Chora mstari mlalo kutoka $CF=30$ hadi uingiliane na ogive.
• Kutoka sehemu ya makutano, chora mstari wima chini hadi mhimili wa x (Height).
• Thamani kwenye mhimili wa x ambapo mstari wima unakatiza ndiyo asilimia ya 30.

Kwa kutumia fomula ya kukokotoa asilimia (interpolation) kwa darasa la 35-39 (ambapo CF inatoka 17 hadi 35):

Ambapo $L = 34.5$ (mpaka wa chini wa darasa), $N = 100$, $CF_b = 17$ (CF kabla ya darasa), $f_p = 18$ (masafa ya darasa), $c = 5$ (upana wa darasa).