Question

Explain the main limitations of statistics.​

Answer 1

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■ Some important limitations of statistics are:–

(1) Statistics laws are true on average. Statistics are aggregates of facts, so a single observation is not a statistic. Statistics deal with groups and aggregates only.

(2) Statistical methods are best applicable to quantitative data.

(3) Statistics cannot be applied to heterogeneous data.

(4) If sufficient care is not exercised in collecting, analyzing and interpreting the data, statistical results might be misleading.

(5) Only a person who has an expert knowledge of statistics can handle statistical data efficiently.

(6) Some errors are possible in statistical decisions. In particular, inferential statistics involves certain errors. We do not know whether an error has been committed or not.

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Answer 2

Answer:

☘sᴏᴍᴇ ɪᴍᴘᴏʀᴛᴀɴᴛ ʟɪᴍɪᴛᴀᴛɪᴏɴs ᴏғ sᴛᴀᴛɪsᴛɪᴄs ᴀʀᴇ:–

(1) sᴛᴀᴛɪsᴛɪᴄs ʟᴀᴡs ᴀʀᴇ ᴛʀᴜᴇ ᴏɴ ᴀᴠᴇʀᴀɢᴇ. sᴛᴀᴛɪsᴛɪᴄs ᴀʀᴇ ᴀɢɢʀᴇɢᴀᴛᴇs ᴏғ ғᴀᴄᴛs, sᴏ ᴀ sɪɴɢʟᴇ ᴏʙsᴇʀᴠᴀᴛɪᴏɴ ɪs ɴᴏᴛ ᴀ sᴛᴀᴛɪsᴛɪᴄ. sᴛᴀᴛɪsᴛɪᴄs ᴅᴇᴀʟ ᴡɪᴛʜ ɢʀᴏᴜᴘs ᴀɴᴅ ᴀɢɢʀᴇɢᴀᴛᴇs ᴏɴʟʏ.

(2) sᴛᴀᴛɪsᴛɪᴄᴀʟ ᴍᴇᴛʜᴏᴅs ᴀʀᴇ ʙᴇsᴛ ᴀᴘᴘʟɪᴄᴀʙʟᴇ ᴛᴏ ǫᴜᴀɴᴛɪᴛᴀᴛɪᴠᴇ ᴅᴀᴛᴀ.

(3) sᴛᴀᴛɪsᴛɪᴄs ᴄᴀɴɴᴏᴛ ʙᴇ ᴀᴘᴘʟɪᴇᴅ ᴛᴏ ʜᴇᴛᴇʀᴏɢᴇɴᴇᴏᴜs ᴅᴀᴛᴀ.

(4) ɪғ sᴜғғɪᴄɪᴇɴᴛ ᴄᴀʀᴇ ɪs ɴᴏᴛ ᴇxᴇʀᴄɪsᴇᴅ ɪɴ ᴄᴏʟʟᴇᴄᴛɪɴɢ, ᴀɴᴀʟʏᴢɪɴɢ ᴀɴᴅ ɪɴᴛᴇʀᴘʀᴇᴛɪɴɢ ᴛʜᴇ ᴅᴀᴛᴀ, sᴛᴀᴛɪsᴛɪᴄᴀʟ ʀᴇsᴜʟᴛs ᴍɪɢʜᴛ ʙᴇ ᴍɪsʟᴇᴀᴅɪɴɢ.

(5) ᴏɴʟʏ ᴀ ᴘᴇʀsᴏɴ ᴡʜᴏ ʜᴀs ᴀɴ ᴇxᴘᴇʀᴛ ᴋɴᴏᴡʟᴇᴅɢᴇ ᴏғ sᴛᴀᴛɪsᴛɪᴄs ᴄᴀɴ ʜᴀɴᴅʟᴇ sᴛᴀᴛɪsᴛɪᴄᴀʟ ᴅᴀᴛᴀ ᴇғғɪᴄɪᴇɴᴛʟʏ.

(6) sᴏᴍᴇ ᴇʀʀᴏʀs ᴀʀᴇ ᴘᴏssɪʙʟᴇ ɪɴ sᴛᴀᴛɪsᴛɪᴄᴀʟ ᴅᴇᴄɪsɪᴏɴs. ɪɴ ᴘᴀʀᴛɪᴄᴜʟᴀʀ, ɪɴғᴇʀᴇɴᴛɪᴀʟ sᴛᴀᴛɪsᴛɪᴄs ɪɴᴠᴏʟᴠᴇs ᴄᴇʀᴛᴀɪɴ ᴇʀʀᴏʀs. ᴡᴇ ᴅᴏ ɴᴏᴛ ᴋɴᴏᴡ ᴡʜᴇᴛʜᴇʀ ᴀɴ ᴇʀʀᴏʀ ʜᴀs ʙᴇᴇɴ ᴄᴏᴍᴍɪᴛᴛᴇᴅ ᴏʀ ɴᴏᴛ.